@article{AIHPC_1996__13_1_17_0, author = {Horozov, Emil Ivanov and Iliev, Iliya Dimov}, title = {Perturbations of quadratic hamiltonian systems with symmetry}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, volume = {13}, year = {1996}, pages = {17-56}, mrnumber = {1373471}, zbl = {0854.34035}, language = {en}, url = {http://dml.mathdoc.fr/item/AIHPC_1996__13_1_17_0} }
Horozov, Emil Ivanov; Iliev, Iliya Dimov. Perturbations of quadratic hamiltonian systems with symmetry. Annales de l'I.H.P. Analyse non linéaire, Tome 13 (1996) pp. 17-56. http://gdmltest.u-ga.fr/item/AIHPC_1996__13_1_17_0/
[1] Le groupe de monodromie du déploiement des singularités isolées de courbes planes I, II. I: Math. Annalen, Vol. 213, 1975, No. 1, pp. 1-32; II: In Proc. Int. Congr. Math., (Vancouver, 1974), Vol. 1, 1975, pp. 395-404. | MR 377108 | Zbl 0352.14011 | Zbl 0316.14011
,[2] Geometrical methods in the theory of ordinary differential equations, Springer Verlag, Berlin, Heidelberg, New York, 1988. | MR 947141 | Zbl 0648.34002
,[3] Singularities of differentiable maps II, Birkhäuser Verlag, Basel, 1988. | MR 966191
, and ,[4] A class of planar quadratic vector fields with a limit cycle surrounded by a saddle loop, Proceedings of the AMS, Vol. 288, 1983, pp. 719-724. | MR 702307 | Zbl 0521.58046
,[5] On the number of limit cycles which appear with the variation of the coefficients from an equilibrium position of focus or center type, Amer. Math. Soc. Transl., Vol. 100, 1954, pp. 1-19. | MR 59426 | Zbl 0059.08201
,[6] Bifurcation of the limit cycle of a family of planar vector fields, Selecta Math. Soviet., Vol. 1, 1981, pp. 373-387, Russian original Trudy Sem. I. G. Petrovskogo, 1976. | MR 442988 | Zbl 0518.58029
,[7] A survey of quadratic systems, J. Differential Equations, Vol. 2, 1966, pp. 293-304. | MR 196182 | Zbl 0143.11903
,[8] The period function of a Hamiltonian quadratic system, Diff. Int. Equations, Vol. 6, 1993, No. 6, pp. 1357-1365. | MR 1235199 | Zbl 0780.34023
and ,[9] Abelian integrals for quadratic vector fields, J. reine angew. Math., Vol. 382, 1987, pp. 165-180. | MR 921170 | Zbl 0621.58033
, and ,[10] The International Dictionary of Applied Mathematics, D. van Nostrand Company Inc., Princeton, New Jersey, 1960. | MR 116566 | Zbl 0099.00103
(Editor),[11] Limit cycles and zeroes of Abelian integrals satisfying third order Picard-Fuchs equations, In "Bifurcations of Planar Vector Fields", Lect. Notes in Math., 1455, J.-P. Françoise, R. Roussarie, eds., pp 160-186. | MR 1094379 | Zbl 0719.34048
and ,[12] Limit cycles of perturbations of quadratic Hamiltonian vector fields, J. Math. Pures Appl., Vol. 72, 1993, pp. 213-238. | MR 1216096 | Zbl 0829.58034
and ,[13] Intersection matrices for certain singularities of functions of two variables, Funct. Anal. Appl., Vol. 8, 1974, pp. 10-13. | MR 338437 | Zbl 0304.14009
,[14] Dynkin diagrams for singularities of functions of two variables, Funct. Anal. Appl., Vol. 8, 1974, pp. 295-300. | MR 430302 | Zbl 0309.14006
,[15] On saddle-loop bifurcations of limit cycles in perturbations of quadratic Hamiltonian systems, J. Differential Equations, Vol. 113, 1994, No. 1, pp. 84-105. | MR 1296162 | Zbl 0808.34041
and ,[16] On the number of limit cycles in perturbations of quadratic Hamiltonian systems, Proc. Lond. Math. Soc., Vol. 69, 1994, No. 1, pp. 198-224. | MR 1272426 | Zbl 0802.58046
and ,[17] Hilbert-Arnold problem for cubic Hamiltonians and limit cycles, In: Proc. Fourth Intern. Coll. Diff. Eqs, VSP Intern. Sci. Publs, Utrecht, 1994, pp. 115-124. | MR 1458390 | Zbl 0843.34037
and ,[18] Number of zeros of certain Abelian integrals in a real domain, Funct. Anal. Appl., Vol. 11, 1978, pp. 78-79. | Zbl 0386.58008
,[19] Double exponential estimate for the number of zeros of complete Abelian integrals, Preprint, June 1994.
, ,[20] Real analytic manifolds with finiteness properties and complex Abelian integrals, Funct. Anal. Appl., Vol. 18, 1984, pp. 119-128. | Zbl 0584.32016
,[21] Global bifurcations and chaotic behaviour in a disturbed quadratic system with two centers (in Chinese), Acta Math. Appl. Sinica, Vol. 11, 1988, No. 3, pp. 312-323. | Zbl 0666.34034
and ,[22] Nonoscillations of elliptic integrals, Funct. Anal. Appl., Vol. 24, 1990, No. 3, pp. 205-210. | MR 1082030 | Zbl 0738.33013
,[23] Über Autoschwingungssysteme, die den Hamiltonischen nahe liegen, Zeitr. der Sowjetunion, Vol. 6, 1934, pp. 25-28. | Zbl 0010.02302
,[24] On the number of limit cycles which appear by perturbation of separatrix loop of planar vector fields, Bol. Soc. Bras. Mat., Vol. 617, 1986, pp. 67-101. | MR 901596 | Zbl 0628.34032
,[25] Estimate of the number of zeros of Abelian integrals depending on parameters and limit cycles, Funct. Anal. Appl., Vol. 18, 1984, pp. 98-108. | MR 745696 | Zbl 0578.58035
,[26] Theory of limit cycles, Translation of Mathematical Monographs, Vol. 66, AMS, Providence, 1986. | MR 854278 | Zbl 0588.34022
et al.,[27] On the number of limit cycles of a class of quadratic Hamiltonian systems under quadratic perturbations, Res. Rept Peking Univ., No. 33, 1993.
and ,[28] Quadratic systems with center and their perturbations, J. Differential Equations, Vol. 109, 1994, No. 2, pp. 223-273. | MR 1273302 | Zbl 0797.34044
,[29] Sturm's theorem for hyperelliptic integrals, Leningrad Math. J., Vol. 1, 1990. | MR 1036839 | Zbl 0724.58026
,